Exercise 2 | Wiskunde op Tilburg University

Consider the production function

$P(L,K)=2L+3K$ . Use elasticity to determine the approximate percentage increase of output if the input of capital is increased by four percent, given that labor remains constant and

$(L,K)=(5,10)$ . (See also Exercise 1.)

Antwoord 1 correct

Correct

Antwoord 2 optie

$\dfrac{3}{4}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$9$

Antwoord 3 correct

Fout

Antwoord 4 optie

$5\frac{1}{3}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$3$

Antwoord 1 feedback

Correct:

$\epsilon_K=P'_K(L,K)\cdot \dfrac{K}{P(L,K)}=3\cdot \dfrac{K}{2L+3K}$ . Therefore, at

$(L,K)=(5,10)$ it holds that

$\epsilon_K=\dfrac{3\cdot 10}{2\cdot 5+3\cdot 10}=\dfrac{3}{4}$ .

Then

$\% \Delta P \approx \epsilon_K \cdot \%\Delta K=\frac{3}{4} \cdot 4=3$ .

Go on.

Antwoord 2 feedback

Wrong: Use that

$\% \Delta K=4$ .

See Partial elasticity.

Antwoord 3 feedback

Wrong:

$\epsilon_K\neq P'_K(L,K)$ .

See Partial elasticity.

Antwoord 4 feedback

Wrong:

$\Delta P \approx \epsilon_K \% \Delta K$ .

See Partial elasticity.